I think this is an interesting question, so I'll make a start on answering it.
Hopefully more people may join in the discussion, it's an interesting puzzle

Let's assume there are 6 players, 1 table, equal stacks and 1 winner.
This is equivalent to a dice roll. Each side of the dice = a player. 1 player wins, the other 5 sides of the dice lose.
For all 6 players to 'balance' their wins in just 6 rolls is somewhat unlikely at a 1.5% chance. (1*(5/6)*(4/6)*(3/6)*(2/6)*(1/6))

A useful question: how many dice rolls on average do I need to roll to get each number once?
Answer: 14.7 rolls
Because:

6

Σ 6/k = 14.7

k=1

The long term average is 14.7, but this will vary from say >=6 to 50 rolls, for example.
It seems to me that you will always have 1 or more 'run bad' players, requiring 14.7 rolls (on average) so they can win at least once.
And if you only win 1 in 15 all-ins, you are still losing.

I ran a program, that is equivalent to 100 tables, 6 players each, who go all-in every hand, until everyone has won at least once.
Here is a histogram of those results:



{y=frequency; x=number of dice rolls, until each win minimum once)

A short random sample, but I like it, it gives you a rough idea of how it could play out.
This 100 iterations turns out to be 1420 all-ins. 80% in the range 9 to 22.
If you went through several 10,000's of iterations the chart would curve more with the high point being at 14.7, which is the maths answer.
When I run a few thousand iterations, the middle 80% seems to fall in the range of 8 to 23 rolls.

But then the question is: how often are the Big Splashes? Is it 1 a day, or 1 a week?
We might have an equal chance of being the guy who wins 1 Big STP out of 15 all-ins. But is that in 15 days or 15 weeks?

Looking at the chart I'd feel sorry for the guy who only won 1 in 39 all-ins, or 20-odd all-ins. And no-one else would believe him because they would be either 'break-even' or 'run good', and would be saying 'it's fine.' lol